The equation of a simple harmonic wave is given by
`y = 3 sin"(pi)/(2) (50t - x)`
where `x` and `y` are in meters and `x` is in second .The ratio of maximum particle velocity to the wave velocity is

Options

A. `(2)/(3) pi`
B. `2 pi`
C. `(3)/(2) pi`
D. `3 pi`

Answer

C

Explanation

`y = "3 sin" (pi)/(2) (50 t - x)`
`y = 3 sin (25 pi t - (pi)/(2) x)`
`y = A sin (omega t - Kx)`
`omega = 25 pi, K = (pi)/(2)`
`2 pi v = 25 pi, (2pi)/(lambda) = (pi)/(2)`
`v = (25)/(2) Hz, lambda = 4` m
Velocity of wave, `upsilon = v lambda = (25)/(2) xx 4 = 50` m/s
Maximum velocity of particle
`upsilon_(max) = omega A = 25 pi xx 3 = 75 pi`
`(upsilon_(max))/(upsilon) = (75 pi)/(50) = (3pi)/(2)`